On the Convergence of Tsetlin Machines for the AND and the OR Operators

Xuan Zhang, Lei Jiao, Ole-Christoffer Granmo

Keywords: Tsetlin Machine, Convergence, AND operator, OR operator

TL;DR: Main text: 9 pages, Appendices: 19 pages, all combined into a single file for easier reference.

Abstract:

The Tsetlin Machine (TM) is an innovative machine learning algorithm rooted in propositional logic, achieving state-of-the-art performance in various pattern recognition tasks. While previous studies analyzed its convergence properties for the 1-bit and XOR operators, this work extends the analysis to the AND and OR operators, completing the study of fundamental digital operations. Our findings demonstrate that the TM almost surely converges to reproduce the AND and OR operators when trained on noise-free data over an infinite time horizon. Notably, the analysis of the OR operator uncovers a distinct property: the ability of the TM to represent two sub-patterns jointly within a single clause, contrasting with its behavior in the XOR case. Furthermore, we investigate the TM’s behavior for AND/OR/XOR operators with noisy training samples, including mislabeled samples and irrelevant inputs. With wrong labels, the TM does not converge to the intended operators but can still learn efficiently. With irrelevant variables, the TM converges to the intended operators almost surely. Together, these analyses provide a comprehensive theoretical foundation for the TM's convergence properties across basic Boolean operators.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 7748